Elliptic curve isogeny class 16.1-a over number field 4.4.19796.1

• Base field: 4.4.19796.1
• Label: 4.4.19796.1-16.1-a
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.19796.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + x + 8 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.19796.1

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a + 1\) , \( a^{2} - a - 4\) , \( a + 1\) , \( 0\) , \( -2 a^{2} - a + 2\bigr] \)
16.1-a2	\( \bigl[a + 1\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -15 a^{2} + 20\) , \( -9 a^{3} - 63 a^{2} + 6 a + 90\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph